contagdiscstate {lacunaritycovariance}

Disc State Contagion

Description

Calculates the disc-state contagion landscape metric as described in (Hingee, 2016; Hingee, 2019). The disc-state contagion landscape metric describes the entropy (mixing) between four possible states of a disc:

1. the disc is completely contained in \Xi

2. the disc does not intersect \Xi

3. the centre of the disc is in \Xi but the disc is not contained in \Xi

4. the disc intersects \Xi but the centre is outside \Xi

Disc-state contagion is a function of the disc radius.

The main difference to classical contagion (O'Neill, 1988) is that disc-state contagion is based on the spherical contact distribution instead of pixel neighbours. One impact of this design is that the distance with which to quantify the mixing between \Xi and the background may be chosen by the user by choosing the disc radius (for classical contagion this distance is fixed by the map resolution).

Note: to create fv objects the function copies about 20 lines of code from the spatstat collection of packages.

Usage

contagdiscstate(XiH, XicH, p, normalise = FALSE)

Arguments

XiH

Conditional spherical contact distribution function for \Xi. Typically this is an fv object but could also be a vector of values. In applications XiH would likely be estimated from a binary map using Hest in spatstat.explore.

XicH

Conditional spherical contact distribution for the complement of \Xi. This is called the Conditional Core Probability in Hingee 2016. Typically this is an fv object but could also be a vector of values. In applications XiH would likely be estimated from a binary map using Hest in spatstat.explore.

p

The coverage probability of \Xi. Can be estimated from binary maps using coverageprob.

normalise

Optional. If TRUE contagdiscstate normalises the results so that all RACS return a value between 0 and 1. Default is FALSE.

Details

XiH should be a function of radius that contains (estimates of) the probability of a disc of radius r not intersecting \Xi if the disc's centre is not in \Xi

\code{XiH}(r) = P(B_r(x) \subseteq \Xi^c | x \in \Xi^c).

Similarly XicH should be (an estimate of) the probability of a disc being fully contained in \Xi given its centre is in \Xi

\code{XicH}(r)\approx P(B_r(x) \subseteq \Xi | x \in \Xi).

These can both be obtained using Hest in spatstat. For XicH take care to apply Hest to the complement of \Xi with the observation window W.

If normalise is TRUE then the result is divided by -2ln(2) and increased by 1 so that contagion will always be between 0 and 1.

Value

If XiH is an fv object then an fv object is returned. If XiH is a vector then the returned object is a vector the same length as XiH with each element corresponding to the contagion at each r value of XiH.

References

Hingee, K.L. (2016) Statistics for patch observations. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences pp. 235-242. Prague: ISPRS.

Hingee, K.L. (2019) Spatial Statistics of Random Closed Sets for Earth Observations. PhD: Perth, Western Australia: University of Western Australia. Submitted.

O'Neill, R.V., Krummel, J.R., Gardner, R.H., Sugihara, G., Jackson, B., DeAngelis, D.L., et al. (1988) Indices of landscape pattern. Landscape Ecology, 1, 153-162.

Examples

xi <- heather$coarse
obswindow <- Frame(heather$coarse)
p <- coverageprob(xi, Frame(xi))
xiH <- Hest(xi, W = obswindow) #Sph. Contact Distrution Estimate
xicH <- Hest(complement.owin(xi), W = obswindow) #Conditional Core Prob. Estimate

contagion <- contagdiscstate(xiH, xicH, p)